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Title: | Accelerated Overrelaxation Method for the Solution of Discrete Laplace’s equation on a Rectangle |
Authors: | Buranay, Suzan Cival Hajan, Bewar Sulaiman A. Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics |
Keywords: | Successive Overrelaxation Method (SOR) Accelerated Overrelaxation Method (AOR) Laplace’s equation 5-point scheme Mathematics |
Issue Date: | 2016 |
Publisher: | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
Citation: | Hajan, Bewar Sulaiman A.. (2016). Accelerated Overrelaxation Method for the Solution of Discrete Laplace’s equation on a Rectangle. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
Abstract: | On a rectangle given the Dirichlet Laplace’s equation, for its solution by finite
differences there exist numerous direct methods and iterative methods. Examples of
direct methods are block decomposition, block elimination, block cyclic reduction
methods, discrete Fourier transform methods. Among the iterative methods,
Successive Overrelaxation Methods, Accelerated Overrelaxation Method (AOM), are
widely used methods.
In this thesis we studied the Accelerated Overrelaxation Method (AOR) for the
numerical solution of discrete Laplace’s equation on a rectangle obtained by 5-point
difference scheme. Numerical results are given for different values of the two
parameters, w and r and for mesh size . h ÖZ: Dikdörtgen üzerinde, Dirichlet sınır koşullu Laplas denklemi verildiğinde sonlu farklar ile sayısal çözümü için birçok doğrudan ve tekrarlama yöntemleri mevcuttur. Doğrudan yöntemlere örnek olarak blok ayrıştırma, blok yok etme, blok döngüsel indirgeme, ayrık Fourier dönüşüm yöntemleri mercuttur. Tekrarlama yöntemleri arasında Successive Overrelaxation yöntemi ve Accelerated Overrelaxation yöntemi sıkça kullanılan metodlardır.
Bu tezde dikdörtgen üzerinde ayrık Laplace denkleminin 5-nokta sonlu fark şeması ile sayısal çözümü için Accelerated Overrelaxation yöntemi çalışılmıştır. Sayısal sonuçlar, 𝑤���� ve 𝑟���� parametrelerinin farklı değerleri için ve adım uzunluğu ℎ için verildi. |
Description: | Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Suzan Cival Buranay. |
URI: | http://hdl.handle.net/11129/4506 |
Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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